Physics-based range estimates for onagers, ballistae, and trebuchets of the Roman era.
Select your siege machine type — Onager, Ballista, or Trebuchet — then enter the projectile mass, launch angle, and stored energy (or counterweight for the trebuchet). Click the calculate button to instantly see the estimated range, maximum height, flight time, and impact energy. Adjust the angle slider or drag coefficient to compare scenarios.
Switch between tabs to compare how the three main Roman siege engines perform with similar parameters. All results use projectile physics with optional aerodynamic drag.
Roman siege warfare was a precise, engineered science — not the wild Hollywood spectacle we often imagine. Understanding catapult range helps historians, re-enactors, game designers, and military history enthusiasts appreciate the tactical decisions Roman generals actually faced.
A typical Roman onager hurling a 10 kg stone could achieve around 300–400 metres of range, which determined how far back the enemy could safely camp their own forces. At the siege of Jerusalem in 70 CE, Josephus recorded catapult stones traveling "two furlongs" — roughly 370 metres — and killing men who didn't hear the warning call in time. Ballistae were precision weapons: their tight bolt groupings at 100–200 metres made them the Roman equivalent of a sniper rifle, capable of targeting specific individuals on walls. Trebuchets, used in later campaigns and adapted from Eastern designs, could hurl 100 kg boulders over 200 metres with devastating wall-breaching energy. These ranges dictated siege line placement, tower heights, shield wall formations, and how Roman engineers dug approach trenches to minimize exposure time.
All three machines use projectile motion physics with energy conversion as the base model. The stored mechanical energy converts to kinetic energy of the projectile, then standard trajectory equations give range and height.
Where η is mechanical efficiency (onager ≈ 0.50, ballista ≈ 0.65, trebuchet ≈ 0.70), E is stored energy in Joules, m is projectile mass in kg, θ is launch angle, and g = 9.81 m/s². For trebuchets, the energy is estimated from counterweight potential energy: E = M_cw × g × 2 × L_arm × efficiency. Aerodynamic drag applies a velocity-dependent reduction factor based on the projectile's drag coefficient and approximate cross-sectional area estimated from mass.
Historical and experimental evidence suggests onagers achieved 250–450 metres with 5–15 kg projectiles, while ballistae could reach 300–500 metres with lighter bolts under ideal conditions. Modern reconstructions at Carnuntum and other sites have confirmed ranges of 300–370 metres for stone-throwing catapults. Ancient texts like Vegetius and Josephus describe ranges consistent with these estimates.
An onager (Latin for "wild ass") is a torsion-powered single-arm sling catapult that lobs projectiles in a high arc — ideal for hitting behind walls. A ballista is essentially a giant crossbow using two torsion springs, firing bolts or stones on a flat, accurate trajectory. The ballista prioritizes precision while the onager prioritizes throwing power and high-angle delivery.
Romans used counterweight siege engines occasionally in the later Imperial period, but the classic trebuchet was more associated with medieval European and Byzantine warfare from the 6th century onward. Roman siegecraft primarily relied on torsion engines (onager, ballista) rather than gravity-powered counterweight machines. The trebuchet option is included for comparative and educational purposes.
Not all stored energy transfers to the projectile. Rope stretch, frame flex, air resistance during the arm's swing, and sling inefficiency all cause energy loss. Experimental reconstructions have measured onager efficiency between 45–55%, ballista around 60–70%, and trebuchets around 65–75%. These figures are built into the calculator's default efficiency values for each machine type.